Introduction: Why Angles of Elevation and Depression Matter
Before GPS and smartphones, surveyors, architects, and navigators needed to measure heights and distances they couldn't directly access. Their solution? Trigonometry. By measuring an angle and one known distance, they could calculate heights of mountains, depths of valleys, or distances across rivers.
In this subtopic, you'll learn two key angle types used in real-world trigonometry problems, plus how to work with bearings for navigation. These concepts appear regularly in IB exams , often combined with the sine and cosine rules you've already studied.
Imagine you're standing at the base of a lighthouse. You can't climb it to measure its height, but you can step back a known distance and measure the angle at which you have to tilt your head upward to see the top. That angle, combined with the distance, is all you need.
Angle of Elevation
Angle of Elevation: The angle formed between the horizontal line of sight and a line of sight directed upward toward an object. It is always measured from the horizontal up to the line of sight.
When you look up at a tall building, a mountain peak, or a flying plane, the angle your line of sight makes with the horizontal is the angle of elevation.
The horizontal line of sight is always your reference , the angle of elevation is measured from this horizontal line upward to the object. It is never measured from the vertical.